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Proton structure function measurements at HERA
Vladimir Chekelian (MPI for Physics, Minich) on behalf of H1 and ZEUS

-

The HERA ep collider (1992-2007) Deep Inelastic Scattering (DIS) / Structure functions (SF) Combination of H1 and ZEUS inclusive NC & CC cross sections QCD fit to the combined H1 and ZEUS data Longitudinal structure function FL(x,Q2) Summary

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HERA (1992­2007)
H1 Integrated Luminosity / pb-1

400

Status: 1-July-2007
electrons positrons low E

low Ep running

Ep = 920 (575, 460) GeV

e
HERA-2

+

300

(2003-2007) peak luminosity 5 1031 cm-2 sec-1 Q2max = 105 GeV2 min ~ 1/1000 rproton longitudinal e-beam polarisation
HERA-1

200

e
100

-

(1992-2000)

H1+ZEUS in total ~ 1 fb

-1

e e
0 0
+

-

e

+

e
500

+

about equally shared between - experiments (H1, ZEUS) - e+ and e-, - positive and negative Pe

1000

1500

Days of running

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Deep Inelastic Scattering (DIS)
Neutral Current (NC) : e± p e±X
H1 P

q k k' Q2 = -q2 = -(k-k')2 virtuality of *,Z Bjorken x x = Q2/2(Pq) y = (Pq)/(Pk) inelasticity Q2 = sxy s=(k+P)
2

Charged Current (CC) : e± p X
ZEUS

Factorisation:

DIS

^ pdf ( x)

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^ - perturbative V.Chekelian, Proton SF at HERA QCD cross section 3 pdf - universal parton distribution functions


NC:
d
± 2 ep NC 2

Proton Structure Functions
2 y Y - xF (x, Q2 ) 2 2 F2 (x, Q ) - FL (x, Q ) 3 Y+ Y+

2 2Y+ ± 2 2Y+ r = = 4 4 dxdQ xQ xQ
Y± = 1 ± (1 - y)
2

helicity factors:

dominant contribution :

F2 ( x, Q2 ) =
at high Q2 (



2 eqi x(qi + qi )

MZ2 ) :

xF3 ( x, Q2 ) = x Bi (qi - qi )
valence quarks

at high y :

e-p e+p

FL

directly sensitive to gluon

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CC:

Flavour Separation
3

2 ± 4 d CC(e p) = G2 M W 1 1[Y +W - y2W Y - xW F 2 L 2x (Q2+ 2 )2 2 dxdQ2 MW

]

~CC(x,Q2)

- reduced CC cross section

e+p

The CC e+p cross section - determines d quark at high x
(little sensitivity from NC)



e+ p CC

( x, Q 2) ~ (u + c ) + (1 - y ) 2(d + s )

The CC e-p cross section - dominated by u quark



e- p CC

( x, Q 2) ~ (u + c) + (1 - y ) 2(d + s )

- constrain d (u) quark density - free of nuclear corrections and isospin assumptions
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Kinematic Reach in x and Q2
HERA: 6 decades both in x and in Q
2

All HERA I (1994-2000) inclusive NC & CC analyses are completed and published - for Q2 < 100 GeV2 the results are final HERA II (203-2007) NC & CC at high Q2 are beeing analysed / published - including polarisation dependences H1 and ZEUS performed new NLO QCD fits (H1PDF 2009, ZEUS09) combination of H1 and ZEUS NC & CC data (HERA I) NLO QCD fit using combined H1 & ZEUS data (HERAPDF0.2) FL measurements using low Ep data

HERA

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Combination of H1 and ZEUS
The goal is to have "the unique HERA data set" which includes expert knowledge in the treatment of the correlations between many individual data sets from H1 and ZEUS most precise, complete and easy to use Combine inclusive unpolarised NC & CC cross sections from H1 and ZEUS at HERA I (1994-2000) all HERA I analyses are completed and published. Exploit differences between H1 and ZEUS in detectors, methods and systematics to "cross-calibrate", and hence to reduce the systematic uncertainties.
for each channel move measured points to a common x-Q2 grid correct Epbeam=820 GeV data to Epbeam=920 GeV average H1 and ZEUS points at given x,Q2 at y < 0.35 keep all data points at y > 0.35, modifying them to account for the determined shifts in the correlated systematic sources.

The averaging exploits a concept of correlated syst. errors, assuming that systematic uncertainties are proportional to expected values and statistical uncertainties are defined by sqrt of expected number of events:

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Combination of H1 and ZEUS data from HERA I
1402 points are combined to 741 unique cross section measurements 2/ndf = 637/656 the original H1 and ZEUS data are fully consistent
110 corr. syst. sources from individual data sets 3 correlated errors from averaging procedure: - difference between "multiplicative" treatment of errors and "additive" - photoproduction background - hadronic energy scale

combined data set:

more than just double statistics:

significant reduction of systematics and little difference then how to treat 110 corr. syst. sources in QCD fits - the simplest approach is to added them in quadrature to the uncorrelated errors 8

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V.Chekelian, Proton SF at HERA


Combination of H1 and ZEUS data from HERA I
1402 points are combined to 741 unique cross section measurements 2/ndf = 637/656 the original H1 and ZEUS data are fully consistent
110 corr. syst. sources from individual data sets 3 correlated errors from averaging procedure: - difference between "multiplicative" treatment of errors and "additive" - photoproduction background - hadronic energy scale

combined data set:

more than just double statistics:

significant reduction of systematics and little difference then how to treat 110 corr. syst. sources in QCD fits - the simplest approach is to added them in quadrature to the uncorrelated errors 9

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Combined H1 and ZEUS data from HERA I
NC e+/-p CC e+/-p

statistics limited

0.05 < Q2 < 30000 GeV

2

~1% total uncertanty for 20< Q2 <100 GeV2 systematics smaller than statistical error

precision data:

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V.Chekelian, Proton SFused as a can be at HERA

10 sole input to the QCD Fit


NLO QCD fit using combined H1 and ZEUS data
input: the combined H1 and ZEUS inclusive NC & CC e+p & e-p data from HERA I next-to-leading order (NLO) DGLAP in MS scheme for evolving PDFs to arbitrary Q2 improved theoretical treatment of heavy flavours which takes the quark masses into account SF calculations in General-Mass Variable Flavour Scheme (GMVFNS): massive NLO splitting and coefficient functions according to Thorne-Roberts VFNS 2008 renormalisation and factorisation scales : Q Q2
min 2

= 3.5 GeV2, Mc=1.4 GeV, Mb=4.75 GeV, s(MZ)=0.1176 (PDG 2006)

Paramaterisation form at starting scale Qo2 =1.9 GeV2 :
2 xf(x, Qo ) = AxB(1- x)C (1+ Dx + Ex2 )
xU=xu+x c, xD=xd+x s+xb c c, bb are genarated dynamically

The optimum number of parameters is taken from saturation in the improvement of the 2 require all PDFs to be positive and qval > qbar at high x 10 free parameters for the central fit: 2/ndf=576/592
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HERAPDF0.2
PDFs
experimental uncertainty (red):
tolerance 2 = 1 110 syst. errors are combined in quadrature with unc. errors 3 sources of errors from the averaging procedure are offset small effect when 110 syst. errors treated as correlated: different methods of treating the correlated systematic errors (Hessian, offset, add in quadrature) do not make much difference

model uncertainty (yellow):
variations of input assumptions added in quadrature

parameterisation uncertainty (green):
make envelope from other 11 parameter fits with Eu > Positivity of PDFs and qval effect is mostly at large 10 parameter fits and 0 and an extra D or E. > qbar at high x are not required. x

gluon and sea are devided by a factor of 20

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Comparison with CTEQ and MSTW

- comparison at 68% CL - HERA QCD fit: impressive precision at low x
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Projection to the LHC
Rapidity dependence of W+ and Z production (at 14 GeV)

errors include only experimental uncertainty experimental (total) uncertainty at central rapidity is ~1% (~2%) when the combined HERA data are used 14th Lomonosov conf. Moscow 25.08.2009 V.Chekelian, Proton SF at HERA 14


The longitudinal structure function FL(x,Q2)
- FL is a pure QCD effect which allows to make critical tests of the perturbative QCD framework used for pdf determinations - FL is directly sensitive to gluon density

F2 ~ L in QPM

p

+

p T

, FL ~ Lp

0

FL

F2

Breit frame:

due to helicity and angular momentum conservation for spin Ѕ quarks

FL ~

L

p

=0

FL = F2-2xF1 = 0
Callan-Gross relation

in QCD:
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FL ( x, Q ) = s x 4
2

2



1

x

dz z3

16 x 2 F2 + 8 eq (1 - ) xg z q 3
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V.Chekelian, Proton SF at HERA


Measurement strategy for FL

NC

d =
2

2 2 y FL / = F2 - 4 Y + 2 1 + (1 - y ) dxd Q xQ
ep NC 2

2

sensitivity to FL only at high y

one possible way:
measure at high y and assume F2
FL published by H1 making assumptions on F2

free from theoretical assumption:

measure at the same x & Q2 and different y by changing the proton beam energy : y = Q2/4EpEex (Ep = 460, 575, 920 GeV)
V.Chekelian, Proton SF at HERA

FL

y 2 /( 1 + (1 - y ) 2 )
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NC cross sections and FL& F2
Ep= 460,575,920 GeV



NC

= F2 - y 2 /(1 + (1 - y ) 2 ) FL
determine FL and F2 from linear fits at each x and Q2

ZEUS

F2 F2

}

FL

FL

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FL(Q2) and recent theory predictions
FL is measured for Q2 from 2.5 to 800 GeV2
FL(Q2) is above zero and consistent with NLO QCD at Q2 > 10 GeV2

x value for each FL(Q2)

FL

FL measurements are above some averaged R=FL/(F -F )=0.18+0.07-0.05 14th Lomonosov conf. 2 L V.Chekelian, Proton SF at HERA 18 NLO QCD calculations at Q2 < 10 GeV Moscow 25.08.2009

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Summary
HERA (1992-2007) finished operation two years ago, after 15 years of data taking all HERA I (1994-2000) NC & CC inclusive analyses are completed and published HERA II (2003-2007) analyses are in progress / beeing published A model-independent averaging method has been developed to combine H1 and ZEUS inclusive NC & CC cross section measurements (applied to the final HERA I data) unique HERA I data set - complete, precise and easy to use significant improvement of systematics (more than just double statistics) HERAPDF0.2 is the NLO QCD fit to the combined H1 and ZEUS data from HERA I improved theoretical treatment for heavy flavours (TR-VFNS) model and PDF parameterisation uncertainties are considered getting ready for precise prediction at the LHC The longitudinal structure function FL (x,Q2) is measured at HERA for 2.5 Q2 800 GeV2 in a model independent way using low Ep data FL is consistent with NLO QCD at Q2 > 10 GeV2 and with R=FL/(F2-FL) = ~ 0.2 some NLO QCD calculations are below FL measurements at Q2 < 10 GeV2

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HERAPDF0.2 : PDFs at Q2 =10 GeV2

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HERAPDF0.2 : PDFs at Q2 =2,100 GeV2

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Charm and Beaty distribution functions
- charm contribution at HERA up to 25-30% - beauty PDF is important for LHC : bb H Boson Gluon Fusion (BGF)

c,b dynamically produced compare predictions with c,b data at HERA NLO QCD predictions for heavy flavour production agree well with the measurements in DIS

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